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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Online-Zugang: | https://arxiv.org/abs/2412.13080 |
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| _version_ | 1866912755866402816 |
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| author | Girardot, Théotime Lee, Jinyeop |
| author_facet | Girardot, Théotime Lee, Jinyeop |
| contents | We study the time evolution of an initial product state in a system of almost-bosonic-extended-anyons in the large-particle limit. We show that the dynamics of this system can be well approximated, in finite time, by a product state evolving under the effective Chern--Simons--Schrödinger equation. Furthermore, we provide a convergence rate for the approximation in terms of the radius $R = (\log N)^{\frac{1}{2}+\varepsilon}$ of the extended anyons. These results establish a rigorous connection between the microscopic dynamics of almost-bosonic-anyon gases and the emergent macroscopic behavior described by the Chern--Simons--Schrödinger equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_13080 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Derivation of the Chern-Simons-Schrödinger equation from the dynamics of an almost-bosonic-anyon gas Girardot, Théotime Lee, Jinyeop Mathematical Physics Analysis of PDEs We study the time evolution of an initial product state in a system of almost-bosonic-extended-anyons in the large-particle limit. We show that the dynamics of this system can be well approximated, in finite time, by a product state evolving under the effective Chern--Simons--Schrödinger equation. Furthermore, we provide a convergence rate for the approximation in terms of the radius $R = (\log N)^{\frac{1}{2}+\varepsilon}$ of the extended anyons. These results establish a rigorous connection between the microscopic dynamics of almost-bosonic-anyon gases and the emergent macroscopic behavior described by the Chern--Simons--Schrödinger equation. |
| title | Derivation of the Chern-Simons-Schrödinger equation from the dynamics of an almost-bosonic-anyon gas |
| topic | Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2412.13080 |